Can anyone tell me how to solve this problem?
http://codeforces.net/contest/177/problem/G2
Thanks in advance!
№ | Пользователь | Рейтинг |
---|---|---|
1 | tourist | 4009 |
2 | jiangly | 3839 |
3 | Radewoosh | 3646 |
4 | jqdai0815 | 3620 |
4 | Benq | 3620 |
6 | orzdevinwang | 3612 |
7 | Geothermal | 3569 |
7 | cnnfls_csy | 3569 |
9 | ecnerwala | 3494 |
10 | Um_nik | 3396 |
Страны | Города | Организации | Всё → |
№ | Пользователь | Вклад |
---|---|---|
1 | Um_nik | 164 |
2 | maomao90 | 160 |
3 | -is-this-fft- | 159 |
4 | atcoder_official | 158 |
4 | awoo | 158 |
4 | cry | 158 |
7 | adamant | 155 |
8 | nor | 154 |
9 | TheScrasse | 152 |
10 | maroonrk | 151 |
Can anyone tell me how to solve this problem?
http://codeforces.net/contest/177/problem/G2
Thanks in advance!
Название |
---|
This is enhanced version of one problem in ICPC WF 2012: https://icpc.kattis.com/problems/fibonacci
Short editorial for WF 2012: http://www.csc.kth.se/~austrin/icpc/finals2012solutions.pdf
I "guess" matrix exponentiation will do the trick for enhanced version (unproven for now, I didn't have time to analyse further).
Let's calculate for each prefix s[1..i] the minimum fibonacci index minind[i] such that s[1..i] is a suffix of fib[i] and s[i + 1..n] is a prefix of fib[i + 1].
Because the relation
can be written equivalently as:
it follows that $min_ind[i]$ is either ∞ or less than n (because fib[i] has all the prefixes of fib[i - 2]). After that, it is essentially a linear reccurence of type
for all $\i \geq n$ (or n + 2 or smth.).
You basically have to compute DP[n] and DP[n + 1] and occurences_less_than_inf, and then do matrix exp. I think that should work :).